The aim of a color gamut mapping is to redistribute the source colors belonging to a source color gamut (for example the extended color gamut of a film) into a target color gamut (for example the color gamut of a standard television monitor). As the shape and boundaries of a target color gamut are generally different from those of the source color gamut, at least some of the target colors that are obtained after such a mapping are different from their corresponding source colors.
An application area of color gamut mapping is notably video content production and post-production. For example, an original version of a video content need to be converted into specific versions adapted for different types of reproduction or transmission: for example, a specific version for cinema, another for television, and a third one for internet. These different versions can be prepared by manual color correction or/and by application of gamut and tone mapping algorithms.
Among the requirements for color gamut mapping are notably:                preservation of color neighborhood and order, absence of color banding and false contours, in order, notably, to prevent from incoherent reproduction of grey and color ramps;        continuity of color and absence of visible quantization or clipping errors, in order, notably, to prevent from banding and false contours;        separate control for lightness, hue and saturation for keeping the full artistic control on how colors are modified, and for allowing the formulation of a higher, semantic level of artistic intents.        
In order to define a color gamut mapping, a gamut boundary description (GBD) of the source color gamut and of the target color gamut is generally used. Such a GBD of a color gamut defines the boundary surface of this color gamut in a color space. GBDs comprise generally explicit, generic 3D representations such as triangle meshes or volume models. For instance, a GBD of a color gamut can be based on a mesh of triangles, each triangle being defined by its three vertices in the color space of this GBD. These vertices are colors located on the boundary of the color gamut.
As illustrated by dotted lines on FIG. 1 in a RGB color space, in case of a color gamut of a trichromatic display or a trichromatic camera, cusp lines usually correspond to singular lines (“edges”) linking each primary color of this display or camera with a secondary color having this primary color as a component, namely a singular line linking: red with yellow, red with magenta, green with yellow, green with cyan, blue with cyan and blue with magenta. The “cusp line” of a color gamut is a line joining cusp colors. When the color gamut is represented in a color space having a measure for chroma such as Lab or JCh color space, a cusp color is a color of maximum Chroma (i.e. maximum saturation) in a plane defined by a constant hue in this color space. In Lab color space for example, chroma is defined to be the square root of the sum of the squares of a and b, respectively. A plane defined by a constant hue is generally named “constant hue leaf”. More generally, cusp colors correspond to singular points (“vertices”) or singular lines (“edges”) on the boundary surface that limits a color gamut. The cusp line of a color gamut can be generally modeled as a line forming a closed polygon on the gamut boundary of this color gamut.
As illustrated by solid lines on FIG. 1, “rims” of a color gamut correspond to the high-lightness ridges of this color gamut linking the white point of this color gamut to the secondary colors and to the low-lightness ridges linking the black point of this color gamut to the primary colors. For example, a yellow rim of a color gamut starts at the white point and ends at the yellow secondary color. The colors on this yellow rim include white, yellowish whites, pales yellows, saturated yellows and finally the yellow secondary color itself. Such as the cusp line of a color gamut, also the rims of a color gamut include generally singular points, that correspond generally to non-continues curvature of the gamut boundary of the color gamut.
On FIG. 1, cusp lines (dotted lines) and rims (solid lines) of the color gamut are by definition straight lines, because these lines are represented in the RGB color space defined by the device having those primary and secondary colors. The same lines are generally not straight when represented for instance in a Lab color space.
When trying to define a method of color gamut mapping (or algorithm: “GMA”) source colors inside a source color gamut (having its own source cusp line and source rims) into target colors such they are located inside a target color gamut (having its own target cusp line and target rims), in order to take advantage of the whole range of colors in the target color gamut, it is known to define the GMA according different conditions among which the following cusp mapping condition: any source cusp color should be mapped into a target cusp color. Such color mapping methods are known as “cusp color gamut mapping”.
US2007/236761 discloses a mapping method using the cusp colors of a color gamut. Cusp colors are interpolated from primary and secondary colors of the color gamut. In the disclosed method, a color ([0104] “point A”) is mapped (([0104] ‘chroma dependent lightness mapping”) to a mapped color ([0104] “point B”). The mapped color has a lightness that is closer to the lightness of a cusp point of the constant-hue leaf of the color to map ([0104] “lightness compression toward primary cusp point”). This cusp point is that of a target gamut and is identical to the cusp point of a source gamut of the same hue leaf (FIG. 12b: “both cusp points”) after a cusp point mapping in this constant-hue leaf ([0059] “the source primary cusp point is mapped to the destination primary cusp point”) and after mapping of black and white points of the source gamut to the black and white points, respectively, of the target gamut (FIG. 11: “lightness rescaling”). The lightness mapping depends on the unique black point, the unique white point and the unique cusp point in the constant-hue leaf in which the mapping is performed.
A drawback of the color mapping method disclosed in US20070236761 is to be based on a unique cusp point and not at least on two different points, those of source and target color gamuts.
US2005/248784 discloses a color gamut mapping method called shear mapping that maps in a constant-hue LC leaf the cusp of the source gamut to the cusp of the target gamut. However, after the shear mapping, other colors that the cusp colors may still lie outside of the target color gamut. For such a situation, US2005/248784 discloses to further map colors that lie outside the target color gamut to the closest colors of the target color gamut, see FIG. 10 of US2005/248784. The document EP2375719 discloses also such an additional mapping step.
As a whole, the main drawback of all known cusp color gamut mapping methods operating within a constant-hue leaf is the mismatch between a generally linear propagation of the mapping of the cusp colors that is generally used for the definition of a mapping function for other colors of this leaf and the non-plane boundaries (i.e. the curvature) of the source and target color gamuts in the color space in which the mapping is performed, for example the Lab color space. The curvature of the source and target color gamuts is due to the curvature or non-linearity of this color space. For example, in FIG. 1 a color gamut is shown in a RGB space in which it is not curved. In FIG. 2, such color gamuts are shown in CIELab space in which they are now curved. The curvature of a color gamut generally reflects the curvature of the color space in which this color gamut is represented. FIG. 2 represents a source color gamut and a target color gamut in the 3D CIELAB color space. A constant-hue leaf of this color space usually includes the L axis. The white lines shown on this figure are the cusp line of the source gamut and of the target gamut. Some segments of these cusp lines are not straight. Some segments of the rims of the source and target gamut are indicated by white arrows. Those segments are not straight too. As an example, we will consider two specific constant-hue leaves on this figure: a first leaf including the L axis and the source cusp color located at the intersection YS of the cusp line of the source gamut with the segment of the rim of the source color gamut which is indicated by an arrow, and a second leaf including the L axis too and the target cusp color YT located at the intersection of the cusp line of the target gamut with the segment of the rim of the target color gamut which is indicated by another arrow. Within each of these first and second constant-hue leaves, known definition of usual cusp gamut mapping functions to be applied to any source color of this leaf are based on a linear propagation (or in a proportional manner) of the cusp mapping rule(s) fixed specifically for the mapping of cusp colors in this constant-hue leaf. But, as shown on FIG. 2, the indicated segment of the rim of the source color gamut as well as the indicated segment of the rim of the target color gamuts are generally not straight lines in the color space in which the mapping is performed. In fact, generally, the whole boundary of any of the color gamuts, including cusp lines and rims become curved by the non-linearity of the mapping color space, here the Lab color space. In consequence, the rims and cusp lines of a color gamut are generally not included in a single constant-hue leaf but pass through different constant-hue leafs. Therefore, when the definition of a gamut mapping function to be applied to source colors of a constant-hue leaf is based on a linear propagation (or in a proportional manner) of such cusp mapping rule(s), this definition does not take into account the position of cusp colors located out of this constant-hue leaf, notably does not take into account the curvature of the cusp lines and of the rims around this constant-hue leaf. It means that, in fact, the color mapping that is appropriate for a source cusp color in a constant-hue leaf may not be appropriate for another source color of this constant-hue leaf. For example, for a source color lying directly on a segment of a rim of the source color gamut, there may be a mismatch between the non-linear geometrical properties of this segment of rim—being a ridge of the gamut—and the linear association of the mapping function used to map this source color with the mapping of the cusp color of the same constant-hue leaf, when this cusp color does not belong to this rim and therefore does not have the geometrical properties of this rim. These two different colors—i.e. the source color belonging to the rim and the cusp color—would better need different color mapping rules. In other words, when propagated linearly by a shearing operation such as in US2005/248784, lightness information obtained from the cusp colors may be inappropriate to map colors belonging to regions farther away from the cusp line.